# How do you write the quadratic y=-1.8x^2-4.32x+4.896 in vertex form?

May 25, 2015

$y = - 1.8 {x}^{2} - 4.32 x + 4.896$
can be simplified as
$y = \left(- 1.8\right) \left({x}^{2} + 2.4 x + 2.72\right)$
or
$y = \left(- 1.8\right) \left({x}^{2} + 2.4 x\right) + 4.896$

The vertex form of a quadratic is
$y = m {\left(x - a\right)}^{2} + b$
and we have already extracted the $m$ value ($- 1.8$)

Completing the square
$y = \left(- 1.8\right) \left({x}^{2} + 2.4 x + {\left(1.2\right)}^{2}\right) + 4.896 + \left(1.8\right) {\left(1.2\right)}^{2}$

$y = \left(- 1.8\right) \left(x - \left(- 1.2\right)\right) + 7.488$
which is the vertex form with a vertex at $\left(- 1.2 , 7.488\right)$